Solve for z z^2+4=4z

$z^{2} + 4 = 4 z$

Subtract $4 z$ from both sides of the equation.

$z^{2} + 4 - 4 z = 0$

Factor using the perfect square rule.

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Rearrange terms.

$z^{2} - 4 z + 4 = 0$

Rewrite $4$ as $2^{2}$ .

$z^{2} - 4 z + 2^{2} = 0$

Check the middle term by multiplying $2 a b$ and compare this result with the middle term in the original expression.

$2 a b = 2 \cdot z \cdot - 2$

Simplify.

$2 a b = - 4 z$

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = z$ and $b = - 2$ .

${(z - 2)}^{2} = 0$

Set the $z - 2$ equal to $0$ .

$z - 2 = 0$

Add $2$ to both sides of the equation.

$z = 2$

Solve for z z^2+4=4z

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